* "new" / "knew": This is the most likely option, as it makes the sentence grammatically correct and thematically coherent: "The new knew is an improvement because it gives out heat with little coal." Here, "knew" likely refers to a new type of stove or furnace that is more efficient.
* "new" / "gnu": This option is humorous and unlikely in a serious context, but it could be used for a playful or creative writing piece: "The new gnu is an improvement because it gives out heat with little coal."
* "new" / "knew" / "gnu": You could also use a combination of the homophones, creating a more complex sentence. For example: "The new knew is an improvement because it gives out heat with little gnu."
Let me know if you have any other sentences you'd like to explore with homophones!